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A Gelfand model for the Okada algebra

  • Harikrishnan T R
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Abstract

In this paper, we construct a Gelfand model for the Okada algebra On(X,Y) with generic parameters X and Y, on the space of symmetric Okada arc diagrams using a conjugation-type action. The model is constructed inductively by identifying the Okada algebra as a diagram algebra and using the Jones basic construction to obtain a tower of algebras that are themselves Okada algebras at lower levels. We use the model to obtain all the irreducible representations of On(X,Y), indexed by the elements of rank n of the Young--Fibonacci lattice, and identify them with the cell modules of On(X,Y).

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Cite

BibTeXRIS
BibTeX
@misc{t2026gelfand,
  title = {{A Gelfand model for the Okada algebra}},
  author = {Harikrishnan T R},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21607},
  eprint = {2609.21607},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21607},
}
RIS
TY  - UNPB
TI  - A Gelfand model for the Okada algebra
AU  - Harikrishnan T R
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21607
UR  - https://arxiv.org/abs/2609.21607
AB  - In this paper, we construct a Gelfand model for the Okada algebra O_n(X,Y) with generic parameters X and Y, on the space of symmetric Okada arc diagrams using a conjugation-type action. The model is constructed inductively by identifying the Okada algebra as a diagram algebra and using the Jones basic construction to obtain a tower of algebras that are themselves Okada algebras at lower levels. We use the model to obtain all the irreducible representations of O_n(X,Y), indexed by the elements of rank n of the Young--Fibonacci lattice, and identify them with the cell modules of O_n(X,Y).
ER  -